Comparative Study of Selected Electrical Loads Behavior Under Corrected and Uncorrected Crest Factor Conditions

Comparative Study of Selected Electrical Loads Behavior Under Corrected and Uncorrected Crest Factor Conditions

E.O. Ogunniyi, A.B. Giwa, T.Y. Ojebisi

Department of Physics, Bamidele Olumilua University of Education, Science and Technology, Ikere-Ekiti, Ekiti State, Nigeria,

O.M. Afolabi

Department of Physics and Electronics, Adekunle Ajasin University, Akungba-Akoko, Ondo State, Nigeria.

Abstract – This paper presents the effect of crest factor (C.F) on six electrical loads in ac power transmission system, as this quantity plays a vital function on the capability of the electrical loads or equipment. Computers and other non-linear electrical loads draw high crest factor current from uninterruptible power supply (UPS) systems. As a result of this, the effect of high crest factor current or voltage increases the useful/required power (real power) by electrical loads and the power becomes apparent. In these six electrical loads, the higher crest factor of the current or voltage drawn by the loads causes a discrepancy between the apparent power and real power by load.

In this paper, 10kVA crest factor reduction (C.F.R) UPS equipment is constructed to investigate; (1) effect of corrected and uncorrected crest factor on six electrical loads applied to an AC source, (2) method to achieve a low and stable crest factor in the distribution system in order to achieve an improved working function of the electrical loads.

The crest factor measurements results obtained showed clearly that crest factor of each load applied were relatively high which gives rise to higher values of apparent and reactive powers but were sufficiently improved when corrective measure is applied. As a result, a relationship between crest factor and apparent/reactive powers was established, as crest factor (C.F) increases, the apparent and reactive powers relatively increase, thus, minimizing power loss and improving the efficiency of electrical loads.

Keywords: Crest Factor, Electrical loads, Non-linear loads, uninterruptible power supply, Real and Apparent power, working function.

INTRODUCTION

One important quantity to note when dealing with AC transmission is the Crest factor (C.F) of electrical loads applied to AC source. This provides insight about the capability of the equipment and as well the electrical loads applied to an AC source. Crest factor describes the ability of an AC power source to generate current or voltage at a particular level. This paper attempts to define this and explain how it affects electrical loads applied to power system. Crest factor can be used to relate the general effectiveness of a signal.

Crest Factor: crest factor of voltage or current is the ratio of peak to rms values.

CREST FACTOR DERIVATIVES

C.F. = , 1

CF = , where CF is Crest Factor, (Pk) Peak is in volts or amps and (RMS) root mean square is in volts or amps.

C.FPure Sine Wave = 1.414

C.FCurrent drawn by a Desktop Computer = 3

RMS is the effective DC value of an AC signal. Since a DC voltage is essentially constant over time, the work performed at the load for a DC voltage is also constant. However, an AC signal is constantly changing in amplitude over time. Therefore the work done at the load is also constantly changing. So the required effect is to have the DC signal perform the same amount of work as the AC signal.

Peak value of voltage or current is the maximum, or minimum, crest value of the waveform. Equipment damage is possible if the peak value becomes too great, even if the rms value is within allowable limits. Also the peak value of a signal is the magnitude of the largest positive value or negative value.

The higher crest factor of the current drawn by the loads causes a larger difference between the values of apparent power and real power of load. Thus, as crest factor increases, the efficiency of the applied loads diminishes.

The graphical relationship between AC peak, AC RMS and DC is shown figure 1.

Figure 1.0

IDENTIFIED SOURCES OF HIGH CREST FACTOR IN POWER TRANSMISSION

A poor or high crest factor can be the result of either a significant phase difference between the voltage and current at the load terminals or it can be due to a high harmonic content or distorted/discontinuous current waveform or irregular waveform signal in power transmission. Poor load current phase angle is generally the result of an inductive load such as an induction motor, power transformer, lighting ballasts, welder or induction furnace, Induction generators, Wind mill generators and high intensity discharge lightings.

Inductive loads which are source of reactive power (kVAR). This reactive power is the power that magnetic equipment (Transformer, Motor, and Relay) needs to produce the magnetic flux. More kVAR present in the utility system results in a High Crest factor, and a high current (I) present on the wire.

The sources of reactive power in inductive loads that increase Crest factor include;

• Transmission wires/lines
• Induction Motors
• Inductive generators (Wind mill generators)
• High Intensity discharge (HID) lighting. (www.powerstudies.com assessed 2025).

These inductive loads constitute a major portion of the power consumed in industrial complexes.

MAJOR EFFECT OF ABNORMAL CREST FACTOR (C.F) ON SIX ELECTRICAL LOADS

1. Increases heat losses in transformers and distribution equipment due to voltage fluctuations and high current,
2. It reduces electrical appliance life,
3. Unstabilized voltage levels,
4. Decreases energy efficiency.

MATERIAL AND METHOD

HIGH CREST FACTOR REDUCTION

Capacitor installation method of crest factor reduction is adopted in this research so as to decrease the magnitude of reactive power (kVAR), and thus minimize high crest factor to a low and stable value.

A Capacitive Crest factor is applied to electric circuit as a means of minimizing the inductive components of the current and thereby reducing the losses in the supply.

The introduction of Crest factor reduction Capacitor is another method of improving the efficiency of electrical appliances. It is not usually necessary to reach an exact crest factor of 1.414 but a value close to it will be ideal. By installing suitable capacitor into the crest factor reduction circuit, a high Crest factor is reduced and the value becomes nearer to 1.414, which is an ideal crest factor in electrical power transmission and also improve the efficiency of electrical appliances.

SWITCHED CAPACITOR

Type: A.C. switched Capacitors (Non-polarity). Capacity: 2 x 2µF standard type

The switched Capacitor method adopted for this study is to centralize crest factor reduction in applications where plant loading is constantly changing, resulting in the need for varying amounts of reactive power.

An advanced micro-controller base reactive controller measures plant power factor via a single current transformer, and switched capacitors modules in and out of service to maintain a user selected target power factor; typically applied at service entrance or near fluctuating loads.

DESIGN AND CONSTRUCTION METHOD OF CREST FACTOR REDUCTION (CFR)

Crest factor reduction equipment is constructed, a switch capacitor method is adopted, so as to centralize applications where powe plant loading is constantly changing, resulting in the need for varying the amount of Peak voltage, Peak current, RMS voltage, RMS current and the reactive power of different electrical applied loads. It is also resistance to heat and can withstand high voltage values in power transmission, very economical compare to other Crest factor compensative measures (www.alibaba.com 2024).

CREST FACTOR REDUCTION MEASUREMENT/ BLOCK DIAGRAM

AC

NON-REDUCTION REGION

C.F

REDUCTION REGION

CHARGER

AUTO-RELAY SWITCH

DPDT SWITCH

CORRECTION UNIT

LOAD

INVERTER

MEASURING UNIT

TO MEASURING UNIT

Figure 2.0 Crest factor reduction/ measurement block diagram

The diagram above explains the design layout/plan of proposed crest factor reduction equipment. It gives a sketch layout of the connections to be made within the stages of the C.F.R equipment constructed in order to ensure error free circuit arrangement.

THE CREST FACTOR REDUCTION (C.F.R) MEASURING SECTION

This section is the most important aspect of this paper. In this section connections are made in order to measure uncorrected and corrected values for Crest factor on various electrical loads applied AC power transmission.

The output of the Centre-tap-transformer is connected to the input of the C.F.R measuring circuit via Electromagnetic Relay 1, (E.M.R.1) to the circuit. A Double-Throw-Double-Pole (DPDT) switch is connected across the circuit so as to switch between the uncorrected inputs C.F as well as for corrected output C.F values obtained for each load applied for crest factor measurements, while the output of this section is connected through E.M.R.2 to the socket (outlet), where loads are applied for measurement as shown in figure below.

The input load voltage, input load current and uncorrected output load factor values and as well as corrected output load factor values are displayed on the LCD via digital measuring multimeter of the reduction measuring section of the equipment. The corrected and the uncorrected crest factor as well as the reactive power are calculated using crest factor and reactive power formula.

DIAGRAM OF CREST FACTOR REDUCTION MEASURING CIRCUIT

Figure 3.0

Multimeter for measuring RMS and Peak values obtained for voltage and current for each load applied for crest factor measurement.

MEASUREMENT OF CREST FACTOR ON SIX DIFFERENT LOADS APPLIED TO AC SOURCE

Measurement:

The following electrical appliances/loads were selected as case study for this research work; these appliances were supplied with AC through 10kVA crest factor reduction power supply (UPS) equipment at their different maximum power demand.

1. Deep-freezer Refrigerator 4. Sandwich Toasting Machine
2. Desktop Computer Set 5. Electric Incubator
3. L.G Air Conditioner 6. Drilling Machine

The above listed electrical loads will be tested and measured one after the other for uncorrected C.F and for corrected C.F in order to calculate the reactive power generated on loads before and after crest factor correction.

The measurement of crest factor (C.F), Reactive power (Q) (kVAR), Apparent power (S) (kVA), Voltage (V) and current

(I) shall be taken for each load applied. The initial and the required i.e. Uncorrected and corrected crest factor for various loads are calculated, and later illustrated in the tables and graphs.

Load (1)

ANALYSIS OF RESULTS FOR SIX LOADS APPLIED USING CREST FACTOR FORMULA

The following results were obtained for each load applied for crest factor correction measurements.

DEEP-FREEZER REFRIGERATOR

Calculation of Crest Factor before correction (Input Ac) Peak Voltage (VPeak) = 561V

R.M.S Voltage (Vrms) = 255V Peak Current (IPeak) = 22.44A

R.M.S Current (Irms) = 10.20A

Therefore, crest factor (C.F) before Correction

Crest Factor (C.F) = V

C.F before correction is 2.20

Hence, apparent power before correction is, Load Real Power (P) = 2000W = 2kW Load Voltage (Vrms) = 225V

Load Current (Irms) = 10.20A Apparent Power (S) = Vrms x Irms

Where:

S = 225V x 10.20A S = 2601V

kVA = 2 + 2 or, S = 2 + 2

Where kVAR = reactive power (Q)

Therefore,

kVAR = 2 2

Q1 = (2601)2 (2000)2

kVAR1 = 1662.89 or

Q1 = 1.663kVAR

Crest Factor after correction or reduction (C.F.C/R)

Load Real Power = 2000W Vrms = 230V

Irms = 9.20A

Apparent Power (S) = 230V x 9.2A

S = 2116VA

Therefore, Crest factor (C.F) after Correction is;

C.F = Crest Factor (C.F) = V

These calculations were done for electrical loads 2 to 6 and measurement results are tabulated below;

RESULTS AND DISCUSSION RESULTS

The calculated values for uncorrected and corrected crest factor as well as other electrical quantities for each load applied for this research are further illustrated in the following tables.

NOTE: C.F.C = Crest Factor Correction

C.F.D = Crest Factor Reduction

Table 1:

Peak Voltage, R.M.S Voltage, Peak Current, R.M.S Current, Crest Factor (C.F.) before correction for each load applied on AC supply.

Table 2:

Peak Voltage, R.M.S Voltage, Peak Current, R.M.S Current, Crest Factor (C.F.) after correction for each load applied on AC supply.

<td4.68

Table 3:

Apparent Power and Reactive Power before and after Crest Factor Correction (C.F.C) for each load applied on AC supply.

The following graphs were plotted in order to compare the values of data collected for crest factor measurements.

CREST FACTOR/APPARENT POWER

CREST FACTOR/APPARENT POWER Vs. LOAD

UNCORRECTED C.F

LOAD

UNCORRECTED APPARENT POWER (kVA)

CORRECTED C.F

CORRECTED APPARENT POWER (KVA)

Figure 1.0 Corrected and uncorrected Crest Factor (C.F) and Apparent Power (kVA) Vs. Six electrical loads applied for measurement.

CREST FACTOR/REACTIVE POWER

CREST FACTOR/REACTIVE POWER Vs. LOAD

UNCORRECTED C.F

LOAD

UNCORRECTED REACTIVE POWER (kVAR)

CORRECTED C.F

CORRECTED REACTIVE POWER (kVAR)

Figure 2.0 Corrected and uncorrected Crest Factor (C.F) and Reactive Power (kVAR) Vs. six electrical loads applied for measurement.

DISCUSSION OF RESULT

The electrical power supply equipment for reducing high crest factor was designed and constructed. Different measurements on 6 loads were done, and the results showed that at high crest factor, the values of apparent power and reactive power were increased as seen from the calculated value in the table 1 and 2. The Crest factor correction reduced high crest factor values of the six electrical loads applied and lowered reactive powers thereby reducing apparent power values obtained, and thus reducing overheating of loads transformer and improve electrical efficiency of the appliances. As seen from graph 1 and 2, the higher the crest factor the higher the values of apparent power and reactive power of electrical loads, the lower the crest factor in electrical transmission, thus, the lower the apparent power and the reactive power of electrical loads, the more the stability of electrical efficiency.

CONCLUSION

The major focus of this research is to investigate the effect of input crest factor on six electrical loads and to provide corrective measures in order to improve the efficiency of loads applied to an AC source. The crest factor measurements results obtained showed clearly that crest factor of loads applied were relatively high which gives rise to higher values of apparent and reactive powers but were sufficiently improved when corrective measure is applied. As a result, a relationship between crest factor and apparent/reactive powers was established, as crest factor (C.F) increases, the apparent/reactive powers also increase.

By adding suitably corrective measures into the input power supply circuit, the crest factor is reduced and apparent/reactive powers were also improved and thus minimizing power loss and improving the efficiency of electrical loads.

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